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ON TIDES 



AND 



TIDAL ACTION IN HARBORS. 



BY 



Professoe J. E. HILGAED 



OF THE 



UNITED STATES COAST SURVEY. 



M>/ ^fol 



BEPBDITED FEOM THE SMITHSONIAN EEPOET FOE 1874. 



WASHINGTON: 

GOVERNMENT PRINTING OFFICE. 

1875. 



,/ya 



ON TIDES AND TIDAL ACTION IN HARBORS.* 



By Professor J. E. Hilgard, of the U. S. Coast Survey, Washington, D. C. 



Ladies and Gentlemen: I propose to engage your attention this 
evening with the subject of the tides of the ocean and the influence ex- 
erted by tidal currents on our harbors. I shall first briefly describe the 
phenomena of the tides as they present themselves to an observer, then 
consider the physical causes to which these phenomena are due, next 
examine more in detail the phases of the tide on our own coasts, and 
finally describe the tidal hydraulics of the magnificent harbor of New 
York!! 

The most obvious change in the surface of the ocean to be noticed 
upon our shores is the alternate rising and falling regularly twice in 
every day. Closer attention will show that the tides of each day occur 
somewhat later than those of the preceding day, the average time of re- 
tardation being fifty-two minutes, and that this retardation corresponds 
to that of the moon. It will pass as a fair approximation to say, that it 
is high water at New York with a southeast moon, or similarly for New 
Castle, on the Delaware, that high water occurs when the moon is south 
In fact, so closely is the time of tide connected with the position of the 
moon, that in order to give the time of high water upon any day ap- 
proximately it is customary to state the time of high water on the days 
of the new and full moon, when the moon passes the meridian at twelve 
o'clock, nearly. This time is called the u establishment of the port." 
Then, to find the time of high water on any other day, it is only neces- 
sary to add the " establishment" to the time of the moon's meridian 
passage on that day. On closer examination, it will be found that the 
interval between the time of the moon's passage over the meridian and 
the time of high water, called the luni-tidal interval, varies with the 
moon's age very sensibly. Moreover, the elevation at high water and 
depression at low water will not always be the same, but will be great- 
est about the times of new moon and full moon, and least about the first 
and third quarters. The details of these variations will be best traced 
out in connection with the explanation of their causes, to which we will 
now proceed. 

The popular explanation of the tides, as depending on the law of gravi- 
tation, is sufficiently simple, although the complete mathematical inves- 
tigation of the subject, by which we should be enabled to predict their 

* Delivered before the American Institute, January 27, 1871, with revision. 

3 



4 ON TIDES AND TIDAL ACTION IN HARBORS. 

occurrence and magnitude for any place, is encompassed with difficul- 
ties, from causes to which we shall hereafter revert. 

If we conceive the earth to be wholly, or for the greater part, covered 
with water and subject to the attraction of the sun, the force of which 
varies inversely as the square of the distance, it will be obvious, that 
while the whole earth will fall toward the sun with a velocity proportioned 
to the aggregate attraction upon its solid portions, (which is the same as 
if all the matter were collected at its center,) the water nearest to the 
sun being accelerated by a greater force, and being fluid, will approach 
the sun more rapidly than the solid core. It will thus run from all sides 
into a protuberance beyond the form of equilibrium of the earth's attrac- 
tion and rotation, until the pressure of the elevated mass equals the dif- 
ference in the attraction of the sun. Moreover, a similar protuberance 
will be formed on the side opposite to the sun, since the particles of 
water, being solicited by a less force than the solid core, will fall more 
slowly toward the sun, and as it were remain behind. Nor does the fact 
that on the average the earth does not lessen its distance from the sun, in 
the least invalidate the force of this reasoning ; for the deviations from 
the tangential motion of the earth in its orbit are precisely those which 
the earth would move through if falling toward the sun unaffected by 
any other impulse. 

The same considerations hold good in regard to the attraction of the 
moon upon the earth and the waters surrounding it ; for although we are 
in the habit of considering the moon as simply revolving about the earth, 
it must be remembered that the attraction is mutual, that both bodies 
describe orbits about their common center of gravity, and that while the 
moon obeys the attractive force of the earth, the latter equally follows 
that of the former, by which it is at every instant of time drawn from the 
path which it would pursue if that iufluence did not exist by an amount 
precisely equal to the fall corresponding to the moon's attractive force- 
As a necessary consequence of the elevation of the water in the 
regions nearest to and most remote from the attracting body, there 
must be a corresponding depression below the mean level of the sea 
at points distant ninety degrees from the vertices of the protuberances, 
or at the sides of the earth, as seen from the sun or moon. If the latter 
bodies maintained a constant position with respect to the earth, the 
effect would therefore be to produce a distortion of figure in the ocean- 
surface, (assumed to cover the whole earth,) having the form of a slightly 
elongated ellipsoid, the two vertices of which would be the one pre- 
cisely under, the other precisely opposite to, the points at which the 
disturbing body is vertical. This, however, is not the case ; for by the 
rotation of the earth, and the motion of earth and moon in their orbits, 
the direction of the disturbing forces is constantly changing with respect 
to any point on the earth's surface. New points arrive at every instant 
under the zenith and nadir of either luminary, and thus it is that waves 
are produced which follow them round the globe. The highest points 



ON TIDES AND TIDAL ACTION IN HARBORS. 5 

of these waves will remain far behind the verticals of the disturbing 
bodies, because the inertia and friction of the water prevent the rapid 
change of form required, and because, although the elevating force is 
greatest under the vertical, it still continues to act in the same direction 
for some hours after the passage of the luminary, with but little 
diminished force. 

This retardation, which would be sensible under the simple supposi- 
tion of an uninterrupted ocean covering the earth's surface, becomes 
very considerable under the actual circumstances of the case. The 
depth of the sea varies so much, and the form of its basin, taken as a 
whole, is so interrupted by the land, that no regular progressive move- 
ment of the tide- wave can take place, except in the great Southern 
Ocean. At all points on the coast the phases of the tide will follow 
the periodicity of the forces causing them, but at each point, at a greater 
or less interval from the culmination of the sun or moon, according to 
its local position, and the more or less circuitous course taken by the 
tide-wave to reach it. This interval and the actual rise and fall of the 
tide must be determined for each place by special observation. 

LUNI-SOLAR PHASES OF THE TIDES. 

The close relations which the times of high water bear to the times 
of the moon's passage show that the moon's influence in raising the 
tides must be much greater than the sun's. In fact, while the whole 
attraction of the sun upon the earth far exceeds that of the moon, yet 
owing to the greater proximity of the latter, the difference between 
its attraction at the center of the earth and at the nearest or most 
remote point of its surface, which difference alone produces the tides, 
is about two and a half times as great as the difference of the sun's 
attraction at the same points. 

SEMI-MONTHLY INEQUALITY. 

We will now consider the particular phases resulting from the com- 
bination of the lunar and solar tides, and from the varying positions of 
those bodies. There will be two complete lunar tides in every lunar 
day of twenty-four hours fifty-two minutes, and also two complete 
solar tides in every mean solar day of twenty-four hours. These are 
known as the semi-diurnal tides, and constitute the principal variations 
of the sea-level. The combined effect of these two fluctuations will be 
most readily understood by reference to the annexed diagram, in which 
the lunar tide is represented by dashes, the solar by dots, and the com- 
bined or actual tide by a full line. At the time of syzygies, or full and 
change of the moon, the effects of both sun and moon combine together 
to produce the spring-tides, when high water is higher and low water is 
lower than at mean tides by the amount of the solar tide. At quad- 
ratures the high water of the sun will combine with the low water of 



6 



ON TIDES AND TIDAL ACTION IN HARBORS. 



the moon to produce a less fall, and the low water of the sun with the 
high water of the moon to produce a less rise than at mean tides ; and 
we have the neap-tides, the range of whfth is less than the mean range 
by the amount of the solar tide. Thus, at New York, the rise and fall 
at syzygies is 5.4 feet, at quadrature 3.4 feet, the former being the sum, 



SEMI-MONTH LY INEQJJA LIT Y 



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NEW OR FULL 
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QUA.RTEB 





OOTA^T 



the latter the difference of the lunar and solar tides, whence we obtain 
for the effect of the moon 4.4 feet and for that of the sun one foot, or a 
ratio of forty-four to ten. This proportion does not prove to be the 
same in all parts of the world, and even varies considerably in places 



ON TIDES AND TIDAL ACTION IN HARBORS. 7 

not far distant from each other. At Boston the heights are 11.3 and 
8.5 feet, respectively, giving a proportion of seven to one. On the 
Atlantic coast of the United States it averages about five to one, while 
on the east side of the Atlantic Ocean, on the coasts of France and 
England, it is in many parts as three to one. These differences are to 
be ascribed to the fact that the shore and harbor tides which we observe 
have in every instance acquired a greater magnitude than the ocean 
tides, in consequence of the wave having passed over a sloping bottom 
and having been greatly retarded by the effect of friction. A comparison 
of the range of spring and neap-tides, therefore, will not serve as a 
correct measure of the relative effect of the sun and moon, unless the 
effect of friction were taken into consideration, which we are at present 
unable to do for want of a complete knowledge of the configuration of 
the bottom. 

The interval between the moon's meridian passage and the time of 
high water is subject to a variation similar to that of the height. On 
the day after the spring-tides, the top of the solar tide-wave will be 
nearly an hour in advance of the lunar tide- wave, and the two waves 
will combine to make high water earlier than the moon's alone would 
bring it. It will continue to be earlier until the moon's transit is 
later by three hours, or in the first octanr. It then falls back until it 
is latest in the third octant, and again advances, until, at the next 
spring-tides, it reaches its mean period. The mean of all the luni- tidal 
intervals for half a month at a port its called its mean establishment, 
which is used for finding the time of high water on any given day ; and 
tables are constructed from observations at the principal ports for find- 
ing the correction for semi-monthly inequality due to the moon's age. 
Thus, for New York, the mean luni-tidal interval is 8h. 13m., and its 
least and greatest values are 7h. 52m. and 8h. 35m. On the Atlantic 
coast of the United States the range of this inequality is about three- 
quarters of an hour ; on the coasts of France and Great Britain it often 
exceeds one and a half hours. 

DIURNAL INEQUALITY. 

The next variation of the tides to be considered is that dependent on 
the moon's declination. Were that body constantly in the plane of the 
equator, the highest points of the tide-waves would also be in that plane, 
and would consequently produce a series of equal tides at any place 
either north or south of the equator. But it is evident that, when the 
moon ascends to the north, the vertex of the tide-wave will tend to fol- 
low it, giving the highest point of one tide in the northern, and the 
highest point of the opposite tide in the southern, hemisphere. Conse- 
quently, when the moon has a northern declination, the tide at any place 
in the northern hemisphere caused by its upper transit will be higher 
than that caused by its lower transit. (See diagram of diurnal inequal- 
ity.) This variation in the heights has a period of one lunar day, and 



8 



ON TIDES AND TIDAL ACTION IN HARBORS. 



is called the diurnal inequality; it reaches its maximum when the moon 
is at its greatest northern or southern declination, and disappears when 
it is on the equator, and consequently has a half-monthly period. The 
variations of height from this cause produce a corresponding inequality 
in the times of high water. The sun's declination affects the tides in a 
similar manner, but the amount of the disturbance is very small, and its 
period extends over half a year. In long series of observations its effect 
is nevertheless well marked, both in height and time. The diurnal in- 
equality, depending upon the moon's declination, is, on the other hand, 
quite sensible, and in many places constitutes a prominent feature of 
the tides, as on the Pacific coast of North America. 



DIURNAL INEQUALITY 




PARALLACTIC INEQUALITY. 

A further cause in the variation of the height of the tides is the varia- 
tion of the distances of the sun and the moon by reason of the ellipticity 



ON TIDES AND TIDAL ACTION IN HARBORS. 9 

of their orbits. The efficacy of a heavenly body in raising tides is shown 
by theory to be inversely proportional to the cube of the distance. 
Hence the efficacy of the sun will fluctuate between the extremes nine- 
teen and twenty-one, taking twenty for its mean value, and that of the 
moon between forty-three and fifty-nine. Taking into account this 
cause of difference, the highest spring-tide will be to the lowest neap as 
59+21 to 43 — 19, or as eighty to twenty-four, or ten to three ; leaving 
out of consideration the local circumstances of access and depth, which, 
as we have stated, modify those proportions in a marked degree. 

TYPE CURVES. 

The three principal forms of tides are illustrated in the annexed dia- 
gram, which exhibits the tides at New York, San Francisco, and Galves- 
ton for two days from actual observation. Of these, that for San Fran- 
cisco may be taken as the normal type, showing the diurnal inequality, 
while that at New 7 York, as at other ports on the Atlantic coast, is not 
sensibly affected by it. The explanation of this feature is probably to 
be found in the supposition that the tide-wave which advances up into 
the Atlantic Ocean from the continuous tide in the Southern Ocean ar- 
rives on our shores twelve hours later than the direct tide-wave which 
crosses the Atlantic from east to west. In this way the diurnal inequal- 
ity will be eliminated by the superposition "of the two tides, the greater 
high water of the former coinciding with the lesser of the latter, and 
vice, versa, leaving the semi-diurnal tides of equal height. 

TIDE REGISTERS 




The tide at Galveston, on the other hand, furnishes a case of the elim- 
ination of the semi-diurnal tide, leaving as a residual only the diurnal 



10 ON TIDES AND TIDAL ACTION IN HARBORS. 

inequality. It is to be presumed in this instance that the tides reaching 
Galveston through the straits of Florida and through the passage be- 
tween Cuba and Yucatan differ by six hours in their periods, causing 
the low water of one to coincide with the high water of the other, thus 
sensibly destroying the semi-diurnal tides, except in so far as they are 
unequal. This leaves a small tide outstanding, having substantially 
the form of the diurnal inequality, and producing the appearance of the 
M single-day tide," or one high and one low water in every twenty-four 
hours. This residual fluctuation is well marked at times when the 
moon's declination is considerable on either side of the equator, but dis- 
appears almost entirely when the moon is near the equator, since, at 
such times, the diurnal inequality disappears. Tides of this class have 
always a small range ; in the Gulf of Mexico they rarely exceed two and 
a half feet, and the average rise and fall is but one and a half foot. 

The tides on the coasts of the United States have been_ specially in- 
vestigated by Professor Bache, the late Superintendent of the American 
Coast Survey. In connection with that work he organized an extensive 
system of exact tidal observations, for the purpose of ascertaining the 
complicated laws which govern the tides of the seas that wash our 
shores. It will be readily understood that in order to separate the 
effects of the different causes which modify the phenomena, it is not- 
sufficient to observe merely the heights and times of high and low 
water, but that a continuous record of the tides is necessary, as the 
inequalities are constantly shifting their place and magnitude. 

TIDE-GAUGES. 

For this purpose a self-registering tide-gauge is used, by which a 
continuous curve, representing the successive changes in the height of 
water, is traced on paper, moved by clock-work, by a pencil actuated by 
the rising and falling of a float in a vertical box, to which the tide has 
free access. The time-scale is such that every hour is represented by 
one inch, and is pricked into the paper by points on the cylinder which 
moves the paper forward. The scale of heights is so adapted to the 
range of the tide at the place of observation that the extreme range of 
the curve will not exceed the width of the sheet — twelve inches. A con- 
tinuous sheet, sufficient for the record of a whole month, is put on the 
tide-gauge at one time. A complete description of this instrument will 
be found in the United States Coast Survey Report for 1853. [The 
lecturer illustrated the construction of several tide-gauges by means of 
diagrams.] 

In northern ports interruptions are experienced in winter from the 
float-box becoming clogged with ice, and various devices have been 
resorted to for overcoming this difficulty. One of the most effective has 
been that of maintaining a temperature above freezing within the float- 
box by means of a simple heating-apparatus. An arrangement of this 
kind has actually been used on the Fox Islands, in Penobscot Bay. A 



ON TIDES AND TIDAL ACTION IN HARBORS. 11 

stream of water flows slowly from an elevated hogshead through a coil 
iii a large stove, passes down to the bottom of the float-box and up 
again into another hogshead, from which it is pumped up every day by 
the observer into the first one. As but a small elevation of temperature 
is necessary, this arrangement has proved quite sufficient. 

Another arrangement, devised by Mr. Batchelder, of Boston, and 
called by him an "Arctic tide-gauge," is in use at Boston, and has com- 
pared well with the ordinary float-gauge. It consists of a strong iron 
tube, about four inches in diameter, firmly bolted to a wharf or pile. It 
is open at the top, and has at the lower end a nipple, to which an India- 
rubber bag is fastened; the length of the tube being sufficient to allow 
the elastic bag to be always submerged at the lowest stage of the tide. 
The bag is supported by a suitable shelf or cage, and is filled with 
glycerine, which is poured in at the top of the tube. When in this con- 
dition the glycerine rises and falls within the iron tube in proportion to 
the varying height and pressure of the column of water above the rub- 
ber bag, the difference in the height of the two columns being in pro- 
portion to the difference of the specific gravity of the water and the 
glycerine. The parts above described insure protection against floating 
ice^ and prevent congelation within the iron tube. 

A copper tube about three inches in diameter, closed at the bottom 
and open at the top, is placed within the iron tube, and floats in the 
glycerine ; if left free, it would rise and fall with the changing level of 
this liquid. The length of the central tube is a little greater than the 
whole range of the tide. 

Near the upper end of the outer tube there are three spiral springs, 
fixed at the top and united at the bottom by a plate or disk, from which 
the central copper tube is suspended. From a stem fixed to the central 
tube or float, and moving with it, a string or chain leads over a single 
pulley, and gives horizontal motion to the pencil-carriage of the record- 
ing-apparatus. 

The distance that the central tube is to move vertically is adjusted to 
agree with the required range of the pencil upon the record-paper by 
placing within it suitable weights. 

As the glycerine rises or falls in the annular space between the iron 
tube and the central float, the spiral spring at the top is more or less 
extended, the extension being uniform on account of the cylindrical form 
of the float. 

It is not necessary that the India-rubber bag be inclosed in a perfo- 
rated box, for the purpose of preventing oscillation, as it is always sub- 
merged, and the pressure upon it is equal to the weight of the column 
of water, having its base at the bag, and its summit at the mean level of 
the surface-waves. 

A tide-gauge, for observations on an open coast, has been devised by 
Mr. Henry Mitchell, of the Coast Survey. The graduated scale on the 
float is read from the shore by means of a spy-glass, the top of the tube 
serving as index-mark. 



12 



ON TIDES AND TIDAL ACTION IN HARBORS. 



PREDICTION OF TIDES. 

Self-registering tide-gauges have been kept in operation for a number 
of years at different points on both coasts of the United States, in order 
to obtain from them the data for predicting the tides ; and as a result, 
tide-tables have been published by the Coast Survey for some years 
past, giving in advance the times and heights of high and low water for 
all the principal ports in the United States for every day in the year. 
In addition to this, the differences are given by which to find the same 
for intermediate ports. 

A very elaborate discussion of the tides observed at Boston during 
nineteen years, a full lunar cycle, has been made by Mr. William Ferrel, 
of the Coast Survey, and has resulted in representing the actual tides 
with unlooked-for precision. By the introduction of the consideration of 
friction Mr. Ferrel has also succeeded in deriving a value for the mass 
of the moon, which appears to compete in exactness with the values 
obtained by astronomical methods. It is one seventy-seventh part of 
that of the earth. 



EARTHQUAKE-WAVES. 

The tide-gauges being in continuous operation, all other fluctuations 
of the ocean-level besides those produced by the tides are likewise reg- 
istered. The tide-curves of the western coast are frequently found in- 
dented by fluctuations arisingfrom earthquakes. A remarkable instance 
of this kind is given in the aunexed diagram of earthquake-waves, which 

EARTHQUAKE WAVES AT FORT PT, AS RECORDED ON THE SELF-REGISTERING TIDE GAUGE. 
6 h I2 h I8 h 



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recorded the earthquake that destroyed the city of Simoda, in Japan, 
in December, 1854. The upper curve is a reduction from the tide-gauge 
register, while the lower shows the earthquake-waves separated from 



ON TIDES AND TIDAL ACTION IN HARBORS. 13 

the tidal wave. The time required for the transmission of the sea-waves 
from Simoda to San Francisco was twelve hours and thirty-six minutes. 
The distance being 4,500 miles, the transmission of the wave was at an aver- 
age rate of 360 miles per hour. The theory of wave-motion teaches us that 
this velocity will be attained by a free-moving wave in a depth of 1,440 
fathoms, which may be taken as the average depth of the Pacific Ocean 
between Japan and California. It will be observed that the crests of 
the waves occur at intervals of about tweoty-three minutes, correspond- 
ing to a length, from crest to crest, of 150 miles. The height when 
the waves arrived at San Francisco was about eighteen inches from 
hollow to crest, the high waves caused by the original impulse having 
gradually flattened out to that form in their transmission across the 
ocean. 

The great earthquake which occurred in Peru, in August, 186S, was 
likewise recorded on the tide-gauges at San Diego, San Francisco, and 
Astoria. The fluctuation of the ocean was so great in this instance as 
to be very sensible to casual observation, and was noted in Australia, 
at the Sandwich Islands, and at Kodiak, in Alaska. The data obtained 
from these observations, combined with the result before mentioned, 
indicate that the average depth of the Pacific Ocean is about 1,800 

fathoms. 

MOVEMENT OF TIDAL WAVES. 

The waves above described, originating with an impulse atone definite 
point, aud propagated freely through the ocean in every direction, with 
a velocity depending upon the square root of the depth of the sea, may 
serve as good illustrations of the manner in which tides are propagated 
through sounds, bays, and rivers. The following table gives the rate of 
motion for different depths : 

Depth in feet 10 Miles per hour 12. 2 

" 60 " " 30.0 

" " 100 « " 38.7 

" " 1,000 " " 122.3 

" " ... 6,000 " " 299.5 

That movement of the ocean, however, which we have designated by 
the name of tide-wave, does not partake of the nature of a wave in the 
common acceptation of the term, but it is rather to be conceived as a 
general movement of the water toward a point under the attracting body, 
and again away from it. Its periodicity is strictly dependent upon that 
of the attracting body. The velocity of the movement is about 1,000 
miles per hour on the equator ; it extends to the bottom of the ocean, 
the depth of which is inconsiderable compared with the radius of the 
earth. It is not attended by a sensible elevation of the water in mid- 
ocean; and in this respect the characteristic of what we call a wave is 
absent. The movement may be likened to that of an impulse given to 
a very long rigid bar, as of iron. In this case, a sensible time will be 



14 



ON TIDES AND TIDAL ACTION IN HARBORS. 



required for the transmission of the impulse from one end to the other, 
and during its transmission the particles will successively approach to 
each other, by which an infinitesimal elevation and subsidence, after 
the manner of a wave, will be produced. In the same way the trans- 

TIMES AND HEIGHTS OF TIDES ON ATLANTIC COAST OF UNITED STATES 




mission of the movement through the incompressible water of the sea 
is attended with an infinitesimal elevation and recession ; but when the 
movement reaches shallow water, in approaching the shores, the hori- 
zontal motion is partly translated into vertical motion upon the sloping 
bottom; and it is thus that the tides attain sensible vertical height. 



ON TIDES AND TIDAL ACTION IN HARBORS. 



15 



Now, where a bay or indentation of the coast presents itself, opening 
favorably to the tide- wave thus developed, and decreases in width from 
its entrance toward its head, the tide rises higher and higher from the 
mouth upward. This is due to the concentration of the wave by the 
approach of the shores and to the gradual shoaling of the bottom. 

This effect is strikingly illustrated by a generalization of the heights 
of the tides on the Atlantic coast of the United States. That coast 
presents, in its general outline, as represented in the annexed diagram, 
three large bays : the great southern, from Cape Florida to Cape Hat- 
teras ; the great middle, from Cape Hatteras to Nantucket ; and the 
great eastern, from Nantucket to Cape Sable, now known as the Gulf 
of Maine. It will be seen that the tide-wave arrives at about the same 
time at the headlands, Cape Florida, Cape Hatteras, Nantucket, and 
Cape Sable, and that at those points the height is inconsiderable com- 
pared with the rise at the head of the several bays. Thus, at Cape 
Florida the mean rise and fall is only one and one-half of a foot ; at 
Hatteras, but two feet ; while at the intermediate entrance to Savannah 
it reaches seven feet, declining in height toward both capes. Again, at 
the head of the middle bay, in New York Harbor, it reaches five feet, 
while on the southeast side of Nantucket Island it is little over one 
foot. The configuration of the eastern bay is less regular, and the cor- 
respondence of heights is not so obvious. The recess of Massachusetts 
Bay is well marked, the increase in height reaching ten feet at Boston 
and Plymouth. Boiling on eastward along the coast of Maine, it con- 
stantly increases; but the most striking effect of the convergence of 
shores is exhibited in the Bay of Fundy. At St. John's the mean height 
of tide is nineteen feet, and at Sackville, in Cumberland Basin, thirty- 
six feet, attaining to fifty feet and more at spring-tides. 

When the wave leaves the open sea, its front slope and rear slope are 
equal in length and similar in form, but as it advances into a narrow 
channel, bay, or river, its front slope becomes short and steep, and its 
rear slope becomes long and less inclined. Hence arises the fact that 
at a station near the sea, the time occupied by the rise is equal to that 
occupied by the descent ; but at a station more removed from the sea, 
the rise occupies a shorter time than the descent. Thus, in Delaware 
Bay and Biver we have the following relations of the duration and 
height of rise and fall : 



Station. 


Mean rise 
and fall. 


Luni-tidal 
interval. 


Mean duration of — 


Flood-tide. 


Ebbtide. 


Delaware breakwater 


Feet. 
3.5 
6.0 
5.5 
6.0 


h. m. 

8 

9 4 
11 53 
13 44 


h. m. 
6 18 
5 56 
5 24 
4 52 


h. m. 
6 8 


Egg Island light 


6 30 


New Castle 


7 2 


Philadelphia 


7 34 







16 ON TIDES AND TIDAL ACTION IN HARBORS. 

An examination of this table will show, besides the marked increase 
in the height of the tide due to the contraction of the shores from the 
capes up to New Castle, a subsequent loss from friction in a narrow 
channel of nearly uniform character, and correspondingly a rapid propa- 
gation of the tide-wave through the deep water of the bay, and a com- 
paratively slow movement along the narrower channel of the river. At 
the mouth of the bay the duration of rise exceeds that of fall by ten 
minutes, while at Philadelphia it is less by two hours forty-two min- 
utes. When the tide is very large compared with the depth of water, 
this inequality becomes very great ; thus, in the Severn Eiver, at Newn- 
ham, above Bristol, England, the whole rise of eighteen feet takes place 
in one and a half hours, while the fall occupies ten hours. 

TIDAL CURRENTS. 

The agency of tidal currents in producing changes in the entrances 
of bays and harbors is a subject of the first importance to commerce 
and navigation, and has received full attention in the prosecution of the 
American coast survey. The laws according to which the changes 
take place require to be studied by long-continued observation, and 
when the change is for the worse, the means of counteracting it must 
be pointed out. 

As on the average the same amount of water moves inward and out- 
ward with the flood and ebb tides, we might readily suppose that the 
same amount of material is transported either way, and that no impor- 
tant change would take place in the configuration of the bottom. But 
the operation of the flood-stream is very different from that of the ebb- 
stream. We have, as a general feature, an interior basin of some ex- 
tent, communicating with the sea by a comparatively narrow passage. 
The flood-stream, therefore, running with considerable velocity through 
this channel, will, as it enters the basin, spread out and become slow, 
depositing the sand and mud it is charged with, and making extensive 
flats or shoals opposite the entrance. The ebb-stream runs slowly over 
the flats from all directions toward the opening without removing much 
of the deposit, and gradually concentrates in definite narrow channels, 
which it scoops out, and the depth of which will depend in a great de- 
gree on the proportion of the area of the basin to the outlet, or, in other 
terms, on the difference of level which will be reached during the ebb 
between the basin and the ocean, which determines the greatest veloc- 
ity and transporting power reached by the ebb-stream. 

On the bars of most of the sand-barred harbors on our southern coast, 
the place and direction of the channel are frequently changed during 
violent storms ; when the direction of the waves happens to be oblique to 
that of the channel, or when the sea runs directly upon the channel, the 
depth of water may be considerably diminished for the time being by the 
sand rolled up by the waves. But in all these cases it is found that 
the normal depth is speedily restored by the scour of the ebb-tide, which 



ON TIDES AND TIDAL ACTION IN HAKBORS. 



17 



depends upon the unchanged factors of area and form of basin, height 
of tide, and character of the material forming the bar. 

EFFECT OF S1NK1NC STONE-FLEET ON CHARLESTON BAft 




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An interesting instance of this maintenance of the depth of channels 
from a determinate tidal basin is furnished by the eifects of the ob- 
structions placed in the channel over Charleston Bar during the war of 
the rebellion. On the accompanying diagram is seen the " stone fleet " 
sunk in the main channel, which at that time had twelve feet of water 
at low tide where the figure 7 indicates the present depth. There was, 
moreover, another channel, making out more to the southward^ with 
2 T 



18 



ON TIDES AND TIDAL ACTION IN HARBORS. 



nine feet of water, where the figure 3 indicates the present depth. The 
vessels were placed checker-wise, in such a manner as to impede naviga- 
tion, while interfering least with the discharge of the water. The effect, 
nevertheless, was the formation of a shoal in a short time, and the 
scouring out of two channels, one on each side of the obstructions, 
through which twelve and fourteen feet can now be carried at low water. 
The increased water-way thus given to the ebb-tide caused it to aban- 
don the old nine-foot channel on the less direct course to deep water. 
We have here the total obstruction of a channel which was of consider- 
able importance to the southward trade by new conditions introduced 
at a point four miles distant from where the effect w r as produced, and 
we are warned how carefully all the conditions of the hydranlic system 
of a harbor must be investigated before undertaking to make any 
change in its natural conditions, lest totally unlooked-for results be pro- 
duced at points not taken into consideration. 

NEW YORK HARBOR. 

Approaching now more closely to the consideration of the tidal con- 
ditions in New York Harbor, we will examine the progress of the tide- 
wave through Long Island Sound from the eastward to its meeting with 
that entering New York Bay at Sandy Hook. 

TIMES AND HEIGHTS OF TIDES IN LONG ISD. SOUND AND NEW YORK HARBOR. 




/BARNEGAT 



We see from the annexed diagram that about seven and a half hours 
after the transit of the moon high water has advanced just within Block 
Island with an elevation of two feet, and at the same time has just 
passed Sandy Hook with an elevation of four and a half feet. Travers- 



ON TIDES AND TIDAL ACTION IN HARBORS. 19 

ing tlie sound at a rate indicated by the Boinan figures, with increasing 
heights indicated by the Arabic numerals, it reaches SancVs Point 
eleven and a half hours after the transit of the moon with a height of 
seven and seven-tenths feet. The observed time of transmission from 
the Eace to Sand's Point is two hours one minute, and the time com- 
puted from the depths, according to the law developed by Airy, is two 
hours fourteen minutes — a very good approximation, when we consider 
the irregularities in the configuration of the sound, which could not be 
taken into account. Advancing still farther, the height somewhat de- 
clines in consequence of the changes of direction in the channel and 
its shallowness. At Hell Gate this tide-wave is met by that which had 
entered at Sandy Hook, and advanced more slowly, owing to the nar- 
rowness and intricacies of the channel, especially in the East River. 

These two tides, which meet and overlap each other at Hell Gate, dif- 
fering from each other in times and heights, cause contrasts of water- 
elevations between the sound and harbor which call into existence the 
violent currents that traverse the East Kiver. The conditions of the 
tidal circulation through Hell Gate are such, that if there were a parti- 
tion across it, the water would sometimes stand nearly five feet higher, 
and at other times five feet lower, on one side than on the other. In the 
actual case of the superposition or compounding of the two tides the 
difference of level existing at any time is of course much less,- but 
the difference of one foot is often observed within the space of 100 
feet in the most contracted portion of Hell Gate, off Hallett's Point 
Referring now more particularly to the diagram representing Xew 
York Bay and Harbor, it is important to observe that the entrance from 
Long Island Sound is a natural depression or arm of the sea, which is 
not changed by the forces now in operation. The tidal currents which 
flow through it do not change the channel, but are obliged to follow it 
in its tortuous course. The Sandy Hook entrance, on the contrary, is 
characterized by a cordon of sands, extending from Sandy Hook to 
Coney Island, intersected by channels, which are maintained against 
the action of the sea, that tends to fill them up, by the scour of the ebb- 
tide from the tidal basin of New York Harbor. 

Unlike Hell Gate passage, where permanence is the leading charac- 
teristic, the bar and channels of Sandy Hook have undergone continual 
changes within the brief period of our history. The advance of Sandy 
Hook upon the main ship-channel is among the notable and important 
instances of the effect of tidal currents. Within a century it has in- 
creased a mile and a quarter. In the place where the beacon on the 
end of the Hook now stands were forty feet of water fifteen years before 
it was built. The cause of this growth is a remarkably northwardly 
current along both shores of the Hook, running both during the flood 
and the ebb tides with varying rates, and resulting from those tides 
directly and indirectly. 

The best water over the bar is about two miles east of Sandv Hook 



20 



ON TIDES AND TIDAL ACTION IN HARBORS. 



light, in a direct line with the swash channel, which is the second open- 

iug shown on the sketch — above the Hook; the shoal lying botween 

the main or Hook channel and the swash channel being known as 
Flynn's Knoll. The greatest depth over the bar is twenty-two feet at 
mean low water ; and very nearly the same depth can now be carried 
through the swash channel, which formerly was three feet shallower, 

ENTRANCE TO NEW YORK HARBOR 



.NEWARK 




but has deepened since the cross-section between the Hook and Flynn's 
Knoll has been diminished by one-third its area by the growth of the 
Hook. This relative change in the capacity of the channels has not, 
however, affected the depth on the outer bar, which, according to the 
principles above laid down, is dependent mainly upon the area of the 
tidal basin within. 

The depth of twenty-two feet at mean low water, which is now main- 
tained at the entrance through the sands constantly thrown up by the 



ON TIDES AND TIDAL ACTION IN HARBORS. 21 

waves of the sea, may be considered as depending upon tlie following 
elements: 

1st. The large basin between Sandy Hook and Staten Island, includ- 
ing Raritan Bay, which furnishes more than one-half of the whole ebb- 
scour ; 

2d. What is called the Upper Bay, including the Jersey flats and 
Newark Bay; 

3d. The North River, perhaps as far as Dobbs' Ferry, maintaining 
the head of the ebb-current, although not directly taking part in the 
outflow ; and, 

4th. A portion of the sound tide, which flows in through Hell Gate. 

The proportion of the three first divisions in producing the depth of 
channel may be approximately estimated by a comparison of the areas 
and distances from the bar. In order to maintain the depth which we 
now have, it is important that the area of the tidal basin should not be 
encroached upon. In proportion as that is diminished the depth of the 
channels will decrease. 

The flats, just bare at low water, but covered at high tide, form as 
important a part as any other portion, for it is obvious that it is only 
the volume of water contained between the planes of low and high 
water — the " tide-prism" — that does the work in scouring the channels. 
The water on the flats is especially useful by retarding the outflow, 
thus allowing a greater difference of level to be reached between the 
basin and the ocean. 

When we yield to the demands of commerce any portion of the tidal 
territory to be used for its wharves and docks, we must do so with fall 
cognizance of the sacrifice we are about to make in the depth of water 
over the bar ; and in order to form any well-founded judgment in re- 
gard to the effect of such encroachments, it is necessary to be in pos- 
session of the fullest knowledge of all the physical facts involved in 
the problem, and no measure of encroachment should be determined 
upon except in pursuance of the advice of scientific experts. 

A proposition frequently mooted by men of enterprise, and resisted 
by those interested in the welfare of the city of New York, is the occu- 
pation of the Jersey flats from Paulus Hook to Robbins Reef for docks 
and wharves. Without expressing any opinion as to the relative value 
of the gain of accommodation for shipping and the loss of depth in 
the channel, I venture to say that the withdrawal of that area from the 
domain of the tide would occasion a loss of not less than one foot in 
the depth of the bar off Sandy Hook, and certainly not more than two 
feet. 

The part which the fourth division in our classification of the basin 
of New York, that of the East River and Hell Gate passage, plays in 
the outflow of the ebb-tide through the Sandy Hook channels, depends 
less upon the area involved than upon the difference in point of time 
and height of tide in Hell Gate, already adverted to. The westerly 



22 ON TIDES AND TIDAL ACTION IN HARBORS. 

current, usually called the ebb-stream, since it falls in with the ebb- 
streain of New York Harbor, taking place when the sound-tide is 
highest, starts from a level of three and a half feet higher than the 
easterly, and thus a much larger amount of water flows out through 
the Sandy Hook channels than through the narrows at Throg's Neck. 
It is apparent, then, that this portion of the ebb-streain, re-enforcing as 
it does the ebb-stream of the harbor proper at the most favorable 
times, performs a most important part in maintaining the channels 
through the Sandy Hook bar. It may be estimated that the closing of 
Hell Gate would cause the loss of certainly not less than three feet in 
the depth of those channels. 

From what has been said with regard to the meeting of the tides in 
Hell Gate, it will be seen that the violent currents experienced in that 
locality are due to causes beyond our control. The dangers to naviga- 
tion arising from these currents, however, by their setting vessels upon 
the rocks and reefs, may, in a great measure, be done away with by the 
removal of the obstructions, in which work considerable progress has 
already been made. The removal of the reef at Hallett's Point, the 
work upon which is now in progress, will doubtless, in a great degree, 
do away wdth the eddies and under-currents produced by the sharp turn 
which the channel now takes at that point. It is not improbable that 
the successful removal of those obstructions will yet cause the sound 
entrance to be used in preference to the other by the fleets plying 
between European ports and the great commercial metropolis of America. 

Note. — The reader who wishes to enter upon the mathematical treatment of the subject, 
of tides is referred to Airy's treatise on tides and waves, and to the memoirs of Whewell 
and Lubbock, in the Philosophical Transactions of the Royal Society ; and for investiga- 
tions of the laws of the tides on our own coasts, to the papers on that subject by Bache 
and others in the annual reports of the Coast Survey. Among the latter, the lecturer is 
particularly indebted to the "Report on the tides and currents of Hell Gate," by Henry 
Mitchell, 1867, in which the complicated problem of the tidal circulation of New York Har- 
bor is treated with great ability and success, 






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